Mr Dorfman, 57, has been involved in the National Theatre, on London’s South Bank, for several years and is a member of its board.

The Cottesloe Theatre will be renamed the Dorfman Theatre to mark the donation.

Travelex is the world’s largest foreign-exchange specialist, and operates in more than 30 countries. Forbes Magazine placed Mr Dorfman, who is married with three children, at number 828 in the list of the world’s billionaires and estimated him to be worth £760 million.

In 2003 a partnership began between the company and the National Theatre, to sell subsidised £10 tickets. More than one million tickets have been sold through the scheme since.

The project came about after Mr Dorfman was introduced to Sir Nicholas Hytner, the director of the National Theatre, by Susan Chinn, wife of Jewish philanthropist Sir Trevor Chinn.

Sir Nicholas said: "I never dreamt that his involvement with the National would have such a far-reaching and transformational effect.

“I couldn’t be more grateful to him.”

Mr Dorfman said: “I am a huge fan of the energy and innovation the National has achieved in recent years and am delighted to lead from the front in supporting its NT Future redevelopment.

“Individual and corporate support is vital to building on London’s leadership in the arts and I hope others will join me in wanting to build on the National’s role at the heart of modern theatre and sustaining it long into the future.”

Hayden Phillips, chairman of the National Theatre, commented: “His supremely generous gift – the largest donation ever made to the NT – will further the National’s determination and ability to thrive in the coming years.

“I hope it will also act as a spur and inspiration to other philanthropists, as a powerful demonstration of faith in the performing arts.”